1. Field of the Invention
The present invention relates to electron beam lithography and, more particularly, to an electron beam lithographic method and apparatus designed to reduce proximity effects.
2. Description of the Related Art
Recently, an electron beam lithographic apparatus has been used as an apparatus for drawing microscopic patterns on samples such as semiconductor wafers and mask substrates. In the electron beam lithographic apparatus, however, the influences of the proximity effect, i.e., thickening and thinning of patterns due to backscattered electrons pose problems. A ghost method and an exposure correction method, which have recently attracted a great deal of attention as methods of correcting the proximity effects, will be described below.
In the ghost method as the first method of correcting the proximity effects (Reference: Published Unexamined Japanese Patent Application No. 59-921 and G. Owen and P. Rissman, "Proximity effect correction for electron beam lithography by equalization of background dose", J. Appl. Phys. Vol. 54, No. 6 (1983), pp. 3573-3581), patterns are drawn by using a correctly focused electron beam at an incident electron current density Qp (to be referred to as "pattern drawing" hereinafter). Thereafter, the beam is defocused to have a diameter dc, and the inverted patterns are irradiated with the beam at an incident electron current density Qc (to be referred to as "correction radiation" hereinafter). A beam diameter dc and the incident electron current density Qc in a defocus state are set to satisfy equations (1) to (3): EQU dc=2.sigma..sub.c . . . (1) EQU .sigma..sub.c =.sigma..sub.b /(1+.eta..sub.E)1/4 . . . (2) EQU Qc=Qp.times..eta..sub.E /(1+.eta..sub.E) . . . (3)
where .sigma..sub.b is the radius at which the intensity of backscattered electrons becomes l/e, .sigma..sub.c is the radius at which the intensity of the defocused beam on a sample surface becomes l/e, and .eta..sub.E is the backscattering energy coefficient of an underlying material for patterning. For example, the values of .sigma..sub.b and .eta..sub.E are set to be .sigma..sub.b =10 .mu.m and .eta..sub.E 0.7 at an accelerating voltage of 50 kV; and .sigma..sub.b =2.0 .mu.m and .eta..sub.E 0.78, at an accelerating voltage of 20 kV (Reference: P. M. Mankiewich et al., "Measurement of electron range scattering in high voltage e-beam lithography", J. vac. Sci. Technol. B, Vol. 3, No. 1, Jan/Feb 1985, pp. 174-176).
The above-mentioned method, however, has the following problems. In general, when an LSI having a small number of patterns is to be subjected to correction radiation, the number of regions to be subjected to correction drawing is increased, and the number of figures for correction drawing is increased. For this reason, a vector scan type lithographic apparatus or a lithographic apparatus using a variable-shaped beam requires a longer period of time for correction radiation than for pattern drawing. In addition, it takes much time to perform data conversion for forming inverted patterns.
As the second method of correcting the proximity effects, an exposure correction method is known. In this method, the exposure dose of each radiation region is adjusted in accordance with the size and density of a corresponding pattern. In the conventional radiation correction method, an exposure dose is determined by a method using a matrix (Reference: M. Parikh, "Corrections to proximity effects in electron beam lithography", J. App. Phys., Vol. 50, No. 6, Jun. 1979, pp. 4371-4387). According to the above-mentioned matrix method, an optimal exposure dose at each position is obtained by, e.g., obtaining the inverse matrix of a matrix representing the relationship between the exposure dose and the absorbed energy amount in resist at each position.
In the exposure correction method, however, the calculation time for determining an optimal exposure dose is prolonged with an increase in resolution and density of patterns. In the case of the matrix method, since the calculation time is prolonged by the third power of the density of patterns, it becomes practically impossible to determine an optimal exposure dose with an increase in resolution of patterns.
As described above, in the conventional electron beam lithographic method, when the proximity effects are to be corrected by the ghost method, the time required for correction radiation is prolonged, leading to, e.g., a decrease in throughput.
when the proximity effects are to be reduced by the exposure dose correction method, the time required to determine an exposure dose is prolonged with an increase in density of patterns. As a result, it becomes practically impossible to apply the method to an LSI having a large number of patterns.